All traveling wave exact solutions of two nonlinear physical models

Abstract

In this paper, we employ the complex method to obtain all meromorphic exact solutions of complex Schamel–Korteweg-de Vries (S–KdV) equation and modified Zakharov–Kuznetsov (mZK) at first, then find all exact solutions of Eqs. (mZK) and (S-Kdv). The idea introduced in this paper can be applied to other nonlinear evolution equations. Our results show that the complex method is simpler than other methods, and there exist some rational solutions wr,2(z),w2r,2(z),w2r,3(z) and simply periodic solutions ws,1(z),w2s,6(z) which are not only new but also not degenerated successively by the elliptic function solutions. In Section 4, we give some computer simulations to illustrate our main results.